Variational Inequalities in Hilbert Spaces with Measures and Optimal Stopping Problems

Variational Inequalities in Hilbert Spaces with Measures and Optimal Stopping Problems We study the existence theory for parabolic variational inequalities in weighted L 2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L 2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coefficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Variational Inequalities in Hilbert Spaces with Measures and Optimal Stopping Problems

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Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer Science+Business Media, LLC
Subject
Mathematics; Numerical and Computational Methods ; Mathematical Methods in Physics; Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-007-9021-x
Publisher site
See Article on Publisher Site

Abstract

We study the existence theory for parabolic variational inequalities in weighted L 2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L 2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coefficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Apr 1, 2008

References

  • On uniqueness of invariant measures for finite- and infinite-dimensional diffusions
    Albeverio, S.; Bogachev, V.; Röckner, M.

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